Description Logic Knowledge and Action Bases (KABs) have been
recently introduced as a mechanism that provides a semantically
rich representation of the information on the domain of interest in
terms of a DL KB and a set of actions to change such information
over time, possibly introducing new objects. In this setting,
decidability of verification of sophisticated temporal properties
over KABs, expressed in a variant of first-order #-calculus, has
been shown. However, the established framework treats inconsistency
in a simplistic way, by rejecting inconsistent states produced
through action execution. We address this problem by showing how
inconsistency handling based on the notion of repairs can be
integrated into KABs, resorting to inconsistency-tolerant
semantics. In this setting, we establish decidability and
complexity of verification.